Apparatus for controlling the directional solidification of a liquid-solid system

ABSTRACT

The growth of a solid obtained by cooling a liquid solution is observed and controlled by measuring the variation in volume of the solid-liquid system at the time of solidification. The method is applicable to the control of oriented crystallization from an initial crystal seed or epitaxial growth on a substrate having a suitable crystal orientation. The rate of crystallization can be controlled by means of a furnace provided with means for producing regulated thermal gradients, temperature-measuring means, a chamber filled with an inert liquid, an open-topped container filled with the liquid to be solidified and immersed in the inert liquid, the container being suspended from one arm of the beam of an electrobalance.

This is a division, of application Ser. No. 691,989 filed June 2, 1976,now U.S. Pat. No. 4,096,024.

This invention relates to a method for controlling the solidification ofa liquid-solid system and especially a method for controlling the growthof a single-crystal layer in liquid phase. The invention is alsoconcerned with a device for the practical application of the method inaccordance with the invention.

As is already known, accurate measurement and control of liquid-solidtransformation is necessary in order to obtain from the liquid statecrystalline substances which have a high degree of structuralperfection, that is, which have no defects such as twinning, crystalimpurities or microprecipitates. Techniques of the prior art achievethese objectives only to a very partial extent since the phenomenon ofcrystallization is controlled only by means of approximate measurementof the range of temperatures within the sample (in a furnace of theBridgman type, for example). Control of the liquid-solid transformationprocess can really be ensured only on the basis of measurement andcontrol of an extensive quantity which is characteristic of saidtransformation or in other words directly related to the quantity ofliquid which has solidified or crystallized in the course of time.

The direct observation of the limit between the liquid phase and thesolid phase which can be performed by optical means satisfies thecondition stated above but can clearly be employed only for transparentelements.

Similarly, gravimetric methods based on direct weighing of the solidimmersed in the nutrient liquid phase or mother medium of differentdensity, such methods having been described in the article by S. H.Smith and D. Elwell, Journal of Crystal Growth (3,4) (1968), page 471which forms part of the description, result in extensive measurements;however, it has been possible by means of these methods to obtain onlyimprecise observations since there are a number of sources of errorwhich affect the results of the measurements:

the real density of the displaced liquid is unknown since it remains afunction of the concentration gradients,

it is not possible to orient the crystal growth, which consequentlygives rise to multidirectional growth with variable rates according tothe crystal orientation of the interfaces,

there remains the difficulty of eliminating the disturbances introducedby convection currents in the liquid.

The method in accordance with the invention overcomes the disadvantagesdiscussed in the foregoing and makes it possible to measure an extensivequantity related to the liquid-solid transformation and applies to theoriented solidification of an extremely wide range of material, whethersuch material is of the congruent-fusion type or not.

The method according to the invention further permits of real andcontinuous control of the transformation process by either manual orautomatic action.

More precisely, the method for controlling the solidification of aliquid-solid system in accordance with the invention essentiallyconsists in observing the growth of the solid obtained by cooling aliquid solution by measuring the variation in volume of the solid-liquidsystem at the time of solidification.

One preferential application of the method according to the invention isthe control of oriented crystallization in liquid phase which is carriedout from an initial crystal seed or by epitaxial growth on a substratehaving a suitable crystal orientation.

The method for controlling the crystal growth for example utilizes thecontinuous measurement of variations in volume of the liquid-solidsystem during the transformation process. These variations in volume areprimarily due to the difference between the specific volume of the samesubstances in the solid state and in the liquid state: this is the molarvolume of fusion ΔV_(F) in the case of pure substances or the differencein integral molar volumes in the case of mixtures.

Thus the quantitative determination of the crystallized (or solidified)mass as a function of time is possible when the molar volume oftransformation of the material is known. Moreover, even if this quantityΔV_(F) is unknown, the method in accordance with the invention makes itpossible to show and thus to control any possible variations in thegrowth rate which are the cause of many structural defects of thecrystallized solid.

The method in accordance with the invention also makes it possible toregulate the rate of crystallization by producing action on thetemperature of the furnace in which the crystallization takes place aswell as on the thermal gradients which exist within said furnace, as afunction of the measurement of the growth rate of the solid in theliquid phase.

The advantages of the method of control arise from the very nature ofthe parameter being measured which is a characteristic extensivequantity of the phenomenon and therefore representative of thequantities transformed.

The measurement of the liquid volumes can be obtained with a high degreeof accuracy by making use of conventional dilatometric techniques whichare adapted to the experimental conditions of solidification. Thesensitivity of these types of measurements makes it possible to detectmicro-variations in speed of transformation or alternatively to controlthe thickness of a thin-film deposit in the case of deposition byepitaxial growth. The method in accordance with the invention isapplicable both to the solidification of either pure or low-alloyedsubstances and to the solidification of binary or more complexconcentrated mixtures.

In the two cases just mentioned, it is known that the variations intransformation volume are only slightly influenced by the progressivevariation of concentrations in each of the two phases in the vicinity ofthe interface. On the contrary, the transformation temperature is anunknown factor since it is largely dependent on the measurement of thesolidification rate, on the nature and concentration of the componentsin the vicinity of the interface. This phenomenon thus accounts for afurther advantage of the method in accordance with the invention.

Similarly, the influence of the mean solidification rate which is laiddown as a result of experience and modifies to a considerable extent thetemperature of transformation by the phenomenon of kinetic undercoolingremains imperceptible in regard to the molar volume of fusion.

Measurement of the variation in solid-liquid volume can be carried outin a preferential embodiment of the invention by immersing thesolid-liquid system in an inert liquid and by measuring the variationsin Archimedean thrust on the solid-liquid system, this variation inthrust being related to the variations in volume of said liquid-solidsystem. There is employed in this case an inert liquid having a lowerdensity than that of the liquid to be crystallized.

In an alternative embodiment of the method according to the inventionand in order to guard against parasitic variations in the volume of thesolid-liquid system and of the enclosure containing said system whichare essentially dependent on the temperature of the liquid melting bath,a preliminary calibration of said variations in volume is accordinglycarried out. This preliminary calibration is performed under conditionswhich are as closely related as possible to those of the realsolidification. Thus the variation in parasitic volume which is notrelated to a liquid-solid transformation can be associated with eachvalue of the temperature and of a temperature gradient. Accordingly,said calibration or preliminary calibration makes it possible in respectof any temperature condition of the liquid bath to be crystallized todetermine the variations in parasitic volume which can accordingly bededucted from the variations in volume to be observed so as to permit ofaccurate determination of the variations in real volume which relate tothe solid-liquid transformation.

In more general terms, the method under consideration which isdesignated as a simulated differential method consists in measuring anelementary parameter on which the system depends and in interpretingsaid parameter independently of the transformation which takes placetherein. Measurement of this elementary parameter (temperature,temperature gradient and so forth) is converted to an electricalquantity such that this latter can be set up in opposition at eachinstant to the voltage delivered by the volume-variation detector. Theresultant signal is thus entirely freed from variations and parasiticfluctuations induced in the system by those of the parameter which ischosen. The elementary parameter or parameters are usually thetemperature of the liquid bath or the temperature and gradient of theliquid bath to be solidified but can also be a vapor pressure,solubility, electrical or optical properties of the bath and so forth.

In the event that a number of parameters are observed, it is possible tostudy the action of each parameter independently, to check thecorrections to be made in each of these parameters and, at the time ofmeasurement of the variation in volume as a function of the differentvalues of said parameters, to correct the variations in volume asmeasured by means of the different variations in parasitic volume inorder to obtain the variations in real volume.

In the case of crystallization, the simulated differential method whicheliminates the parasitic variations in volume of the sample makes itpossible to measure small quantities of the transformation volume alonewith the high degree of accuracy obtained by means of conventionaldilatometric detectors, this being achieved without entailing anyexcessive increase in complexity of the equipment.

Two particularly important applications of the method of control areconcerned in one case with massive monocrystallization from the liquidphase and in the other case with monocrystallization obtained bythin-film epitaxial growth from a saturated liquid phase.

Further properties and advantages of the invention will become morereadily apparent from the following description of practical exampleswhich are given by way of explanation and not in any limiting sense,reference being made to the accompanying drawings, wherein:

FIG. 1 shows the thermal portion of the device for the massivecrystallization of a liquid and for the practical application of theinvention;

FIG. 2 shows the measuring and control portion of the massivecrystallization device shown in FIG. 1;

FIG. 3 shows the curves of time-dependent variations in volume and intemperature obtained by means of the device in accordance with theinvention;

FIG. 4a is an epitaxial cell for making use of the method in accordancewith the invention whilst

FIGS. 4b, 4c, 4d, 4e and 4f show the different stages of operation inthe practical application of the method for obtaining crystal films byepitaxial growth;

FIG. 5 shows a second alternative embodiment of the invention.

The thermal portion of the massive crystallization device is shown inFIG. 1 makes it possible to obtain from a liquid solution 2 a crystal 4which is crystallized from a seed deposited at the bottom of thecontainer 6.

The open-topped container 6 is immersed in an inert liquid 8 containedin a vessel 10.

The container 6 which is totally immersed in the liquid 8 is connectedby means of the wire 12 to the end of one arm of the beam of anelectrobalance which is shown in FIG. 2.

A circulation of gas through the ducts 14 and 16 makes it possible torenew the atmosphere which is present above the bath 8 of inert liquid.

The vessel 10 is placed within a tubular furnace of the Bridgman type;this vertical tubular furnace delivers a centripetal thermal flux; theaxial thermal gradient is increased by means of a winding 18, theintended function of which is to overheat the upper portion of theimmersion bath which is filled with inert fluid 8. The heat sink isconstituted by a cooled probe 20 which is placed in the axis of thefurnace at the lower end of this latter. The arrangement of the vessel10 which contains the inert liquid 8 makes it possible to minimize thevolume of fluid 2 in the liquid state in which the solid sample 4 isimmersed while eliminating surface-active effects produced by the wallson the suspension wire 12 and the container 6.

The bottom portion of the reservoir in the shape of a glove finger makesit possible to increase the radial and axial thermal flux within thesolid-liquid sample.

The temperature is measured by means of the thermocouple 22 in a zonewhich is close to the medium of the container 6. The thermocouple 22 isprotected from external thermal influences by means of an inert mass 24of refractory material. The thermocouple 22 is connected to a correctingunit 56 which is shown in greater detail in FIG. 2.

The thermal gradient which is continuously measured within the inertfluid 8 is maintained constant during the experiment by automaticregulation, this being performed by means of a regulator of known typefitted with a linear programmer 26 which controls the power in the hotregion of the Bridgman furnace and which is well known to those versedin the art. Said programmer 26 controls a thermal regulator 29 which inturn controls the power source 41. A second regulator 28 associated withthe differential comparator 27 for collecting the indications of theregulating thermocouples 33 and 35 produces action on the position ofthe cooling unit 20 in order to stabilize the value of the thermalgradient at a predetermined value.

A system of horizontal screens 30 has the effect of reducing theconvective movements of the atmosphere around the vessel 10.

Measurement of the variations in volume of the two-phase solid-liquidsystem 2-4 which is present within the container 6 is carried out bygravimetry by converting the variations in volume to variations inArchimedean thrust on the container.

In the furnace of the Bridgman type shown in FIG. 1, the value of thethermal gradient and the power programming are adjusted so as to carryout solidification of the sample at different cooling rates.

The possibility of carrying out good measurement of the variations involume of the liquid-solid system calls for very high hydrodynamicstability of the fluids 2 and 8 and also for cancellation by electricalopposition of the factors which influence the response of the balanceother than that which resuts from liquid-solid transformation.

The first condition makes it necessary to establish values of thermaland mass flow which stabilize the fluid masses.

This condition which is undoubtedly favorable to monocrystallization inthe Bridgman technique is satisfied by the application of the principleof the thermal core described in the article by Messrs. H. S. Carslawand J. C. Jaeger, Conduction of Heat in Solids, The Clarendon Press,Oxford, 1967, this article being an integral part of the description.Thus a centripetal horizontal thermal flux and a downwardly orientedvertical axial flux are so applied that the condition of Rayleighstability is maintained at all points of the fluid media.

The second condition is satisfied by adopting the simulated differentialmethod.

The response of the balance during a crystallization operation isinfluenced by a certain number of phenomena: it is necessary to takeaccount not only of the effects which are directly related to theexistence of a transformation volume but also of major parasitic effectswhich are related to variations in density of the liquid, solid and evengaseous masses including the sample and the surrounding bath such asthose produced by variations as a function of the temperature, positionsand dimensions of the container and the suspension wire and also ofsurface tension forces.

This combination of parasitic factors is essentially dependent on theranges of temperature within the device and on its variations.

A comparison of a measurement of temperature which is representative ofthe thermal state of the system at each instant with the indicationsupplied by the balance in the absence of any liquid-solidtransformation shows the linearity and reversibility of the relationexisting between these two quantities within the temperature rangeselected.

It will therefore be necessary only to convert the voltage delivered bythe reference thermocouple 22 to another voltage which can be directlyset up in opposition to that delivered by the electrobalance.

The use of the device for the practical application of the methodaccording to the invention makes it possible to measure the variationand also to control the crystal growth rate (this factor governs thecrystalline quality of the solid) by having recourse to methods ofautomatic control.

The method according to the invention offers the possibility ofmeasuring the solidification rate as a function of time and also servesto control the thermal parameters in dependence on optimum fixed valuesin respect of the rate of solidification in solution.

A further possibility of use of the simulated differential method inaccordance with the invention lies in the direct comparison of thegrowth rates of a sample with the growth rate of a standard reference.For example, it is possible to measure the effect of addition elementson the rate of growth of a sample.

The immersion bath must meet the known requirements of the methods ofunidirectional crystallization, among which can be mentioned:

total relative insolubility of the liquid 8 and of the sample formed inthe liquid 2 and the solid 4,

density of the inert liquid 8 which is lower than that of the generalcontainer sample,

high chemical inertia with respect to these elements in contact and highchemical purity,

excellent wetting properties,

low melting point and low vapor pressure,

molten salt baths of the alkali metal chlorides in a eutecticcomposition, for example, are wholly suitable for metallic solid-liquidsamples. Baths having a base of boric oxide can also be employed.

In FIG. 2, there is shown the electronic diagram in connection with thethermal-gradient furnace for controlling the crystallization of asolid-liquid system. The same elements in FIGS. 1 and 2 are designatedby identical reference numerals.

The arm 50 of the beam of the electrobalance 52 is connected by means ofthe wire 12 to the container 6 in which the solid-liquid system ispresent. Measurement of the force applied to the wire 12 is obtained bycompensation on the solenoid 54 of the other arm of the beam of theelectrobalance 52.

The unit 56 comprises a function module 60, an opposition source 61, anamplifier 62 having a gain G and a differential connection unit 63. Inthis example of construction, a temperature measurement is performed bymeans of the thermocouple at 22 in the vicinity of the container 6.After amplification, the signal which has been processed by the functionmodule acts in opposition to the signal produced by the electrobalancevia channel 54. The signal on channel 66 at the output of the unit 56 isrecorded in the recording unit 67 and the same applies to the signalobtained from a thermocouple 23 which is placed next to the thermocouple22. After calibration, the signal on channel 66 measures the real growthof the solid 4 and can be employed for transmission into the unit 29 forregulating the growth rate as a result of regulation of the furnacetemperatures.

The electrobalance 52 is a conventional "zero" instrument which deliversa voltage which is proportional to the variations in thrust. The signalobtained from the thermocouple 23 may simply be recorded in the unit 67.

The complete assembly consisting of container and liquid-solid samplemust be in equilibrium with the immersion bath prior to commencement ofany transformation process. This assembly must also be freed as far aspossible of gas bubbles which adhere to the surfaces by capillarytension prior to establishment of a base line representing thevariations in parasitic volume in the absence of an actual liquid-solidtransition. In the case of seedless growth, the entirely liquid immersedsample as well as the bath are first placed in a vacuum in order topermit removal of the occluded gases. Under the initial conditions ofthe synthesis to be performed, a temperature stage is then maintainedfor the period of time which is necessary in order to establishequilibrium. The progressive variation of the system is followed bydilatometry and equilibrium is attained when the signal delivered by thedetecting unit (52 and 56) to the channel 66 and recorded in therecording unit 67 no longer varies.

At the end of said temperature stage, the programmed cooling of thefurnace obtained by the regulator 29 is resumed without therebyinitiating the transformation of the sample. The opposition cirucit 61which is incorporated in the unit 56 is calibrated so as to ensure thatthe base line is retained. Crystallization proper can then begin and isindicated by a corresponding progressive variation in the electricaloutput signal on channel 66 which is recorded in the recording unit 67.

A different method can also be adopted for establishing the base line;this method consists in carrying out adjustments during melting of thesamples or dissolving of the solute. Any subsequent deviation from thisline which may be observed during the reverse operation corresponds toan abnormality in the growth rate, this being due either to themechanisms of attachment in the stationary state or to the varioustransient states which may in some cases occur.

Examples of process of crystal growth of an indium-antimonyintermetallic compound:

(a) Physical characteristics of the compound

melting temperature: T_(f) =530±5° C.

density of the solid: ρ_(S) =5.765 [1-1.643×10⁻⁵ (T-530°)]

density of the liquid:

This latter can be linearly related to the temperature by postulating acorrelation factor which is equal to 0.995.

    ρ.sub.1 =6.470[1-1.0267×10.sup.-4 (T-530)]

relative variation in volume at the time of fusion:

    ΔV.sub.f /V.sub.L =12.3%.

(b) Operating conditions

container: tubular crucible of transparent quartz which contains thesample. This sample is constituted by a single-crystal seed which isattached mechanically to the base of the crucible and by apolycrystalline charge which is placed above the seed.

section:1 cm² --height: 10 cm

immersion bath: purified mixture of Li Cl - K Cl having the eutecticcomposition:

Melting point: 355° C.

Density of the liquid: ρ_(e) =1.70[1-3.105×10⁻⁴ (T-355)]

Suspension wire: 10% rhodium-platinum alloy having a diameter of 0.2 mm.

The thermal conditions have been defined in connection with two cases ofsynthesis. The first case corresponds to congruent solidification of thecompound In Sb:

Mean temperature of the sample: 600° C.

Mean thermal gradient: 20° C./cm

Rate of programmed cooling: 15° C./hour.

The second case relates to the crystallization of the stoichiometriccompound from a solution containing 64% by weight of indium, theliquid-solid equilibrium temperature of which is 500° C.

Mean temperature of the sample: 570° C.

Mean thermal gradient: 20° C.

Rate of programmed cooling: 0.6° C./hour.

(c) Measurements

Detection: the electrobalance employed offers a sensitivity of 0.121mV/mg under these operating conditions.

Base line: the signal of the reference thermocouple is amplified with again of 2.330.

Drift of the base line is observed but remains constant and equal to 50μV/hour. The variations observed do not exceed ±2 μV.

Under these conditions of measurement, it has been possible to followthe liquid-solid transformations in both cases with a sensitivity of 10μV, which corresponds to a thickness of 5 μ of formed solid InSb.

In the simple case in which there is observed experimentally bycalibration on the sample in the liquid state a linear variation inthrust as a function of temperature, the mathematical function whichserves to modify the thermocouple signal is of the form: E=A+B S_(TC),where E is the correction potential and S_(TC) is the temperature signaldelivered by the thermocouple 22.

There is then employed as shown in FIG. 2 an adjustable electricopposition source 61 for measuring the coefficient A and a variable-gaindirect-current voltage amplifier 62 for obtaining the coefficient B ofthe formula given above.

In cases in which there is observed a non-linear variation intemperature caused by liquid alloys having a density which does not varylinearly with temperature (this being the case with tellurium-basealloys such as In₂ Te₃, Ga₂ Te₃, for example), processing of thethermocouple signal accordingly utilizes a mathematical function whichis better adapted (polynomial, logarithmic function and so forth). Thistype of treatment of the signal clearly forms part of the device inaccordance with the invention (function module of FIG. 2).

FIG. 3 shows at 200 the curve, recorded as a function of time, of thesignal obtained on channel 26 of the diagram of FIG. 2 comprising thebase line 202 and the corrected signal of resultant force ΔF 204corresponding to solidification in the case of an InSb alloy.Solidification takes place between the points 206 and 208. Thetemperature curve 206 T(t) measured by means of the thermocouple 23 isalso recorded as a function of time.

FIG. 4a shows an epitaxial growth cell and FIGS. 4b, 4c, 4d, 4e and 4fshow the different stages of operation for the deposition of a layer byepitaxial growth on a substrate 70. The epitaxial-growth cell showed inFIG. 4a is employed for the formation of thin films by the method ofhorizontal epitaxy. The epitaxial-growth cell 4a is provided withsliding elements which permits chronological performance of the stagesof operation shown in FIGS. 4b, 4c, 4d, 4e and 4f which will hereinafterbe described. The epitaxial-growth cell 72 of the drawer type has beenmodified so as to conform to the conditions of detection of variationsin volume. The cell 72 can be constructed of graphite or of any otherchemically inert material which is both heat-resistant and capable ofbeing machined with precision. The epitaxial-growth cell which isgenerally designated by the reference 72 has a parallelepipedal shapeand consists of two main elements. One of these latter is a stationaryelement 74 which constitutes the cell body and in which two recesses areformed, the single-crystal substrate 70 being intended to be placed inone recess and a sample 76 employed as a source for saturating thesolution 78 is placed in the other recess.

A moving system referred-to as a drawer is made up of three sections:

a main section 80 comprises the cavity which serves as a reservoir forthe solution 78 and can be positioned with respect to the cell body. Thecapacity of said reservoir is accurately adjusted by displacing a deadspace 84, this displacement being controlled from the exterior of thefurnace 100. Three thermocouples 82 are placed within said dead spacewhich is immersed in the solution during the epitaxial-growth stage. Oneof these thermocouples serves to regulate the furnace 100 whichsurrounds the epitaxial-growth cell. The second thermocouple serves tomeasure the mean temperature of the bath and the third thermocoupleconstitutes the reference element for the system of the simulateddifferential method.

the top portion of the drawer is a sliding plate 86 constituting a coverfor the reservoir on which is fixed the capillary tube 88 of transparentquartz. An end-stop 90 permits the displacement of the plate 86.

Detection of the position of the meniscus within the capillary tube isobtained by means of an optical system constituted by a source 92, afirst lens 94, a lens 96 and a system 98 for measuring the illuminationproduced by the lens 96 such as the sensitive surface of aphotodetector, for example. The optical system forms the image of themeniscus located within the capillary tube 88 on the sensitive surfaceof the photoelectric cell 98. In order to prevent variations in theimage as a result of convection currents of the furnace atmosphere whichsurrounds the cell, this optical sighting operation can be carried outthrough a transparent solid medium such as a quartz rod (not shown inthe figure). The electrical signal at the output of the cell 98 is afunction of all the factors which influence the position of the meniscuswithin the capillary tube 88. The simulated differential method consistsin the case of deposition by epitaxy in generating in opposition to thesignal A delivered by the photoelectric cell 98 another electricalsignal B delivered by the reference thermocouple 82, this signal beingproportional to the displacement of the meniscus independently of theliquid-solid transformation by epitaxial growth.

Thus in the absence of variations in volume resulting from the phasetransformation, the two signals A and B remain equal and opposite duringthe recording which has been defined as the base line. Whentransformation takes place, namely either crystallization ordissolution, a difference appears which is proportional to the masstransformed.

The operating procedure is represented by the different stages in FIGS.4b, 4c, 4d, 4e and 4f. FIG. 4b shows the degassing stage during whichthe cell filled with the single-crystal substrate of the saturationsource and with the bath of predetermined composition containing ifnecessary a doping solute is placed in the vacuum-degassing position.

Adjustment of the base line shown at 202 in FIG. 3 is carried out in theposition shown in FIG. 4c, namely the position of the drawer obtainedafter having adjusted the capacity of the reservoir 78 in order to bringthe meniscus contained in the capillary tube 88 into its initialposition. This adjustment takes place under a number of differenttemperature-variation regimes.

In the stage shown in FIG. 4d, the bath is brought to the initialtemperature which was chosen and contacted with the solution 76 which isa source for the saturation of the solution 78. Contact between thesolution 78 and the substrate 76 is maintained until a physico-chemicalequilibrium between the solid and the liquid is established, thisequilibrium being clearly observed by means of the system for detectingvariations in volume. Homogeneity of the doping agent is obtained in thesame liquid.

FIG. 4e shows the stage of deposition by epitaxy. The bath 78 which issaturated at the suitable initial temperature is placed in contact withthe single-crystal substrate 70. If necessary, a re-adjustment of thephysico-chemical equilibrium can be carried out before initiating theprogram of cooling of the furnace 100 which surrounds the cell. Whencrystallization begins, an optical signal appears and this latter isautomatically converted to a signal which is proportional to thethickness of the deposit on the substrate 70.

The end of the epitaxial growth operation is shown in FIG. 4f. Thus,when the thickness of the layer deposited on the substrate 70 attains apredetermined value, the drawer 86 is brought into the position shown inFIG. 4f in a movement of translation which causes sweeping of thesurface of the layer deposited on the substrate 70, thus removing anyexcess quantity of solution. The complete drawer-type cell is thencooled to room temperature. In one example of execution, namelycrystallization of the In-Sb compound in a thin film, deposition of afilm is carried out from a solution containing 64% by weight of indiumon a substrate having a surface area of 100 mm².

The cross-sectional area of the capillary tube 88 is 1 mm² and the unitfor detecting the displacement of the meniscus permits measurement of alevel different of 10⁻² mm, namely a minimum volume variation of 10⁻²mm³. Taking into account the value of the melting volume of thecompound, this corresponds to a value of 8×10⁻ mm³ of solid formed atthe surface of the substrate, namely a deposit having a theoreticalthickness equal to 0.8 micron.

In the alternative embodiment which has just been described, the inertliquid in which the container is immersed sets temperature limitationswhich may prove objectionable and entails the need for chemicalcompatibilities between the elements in mutual contact and the elementsused as contaminants for the crystal which is being formed. Furthermore,the container for the liquid-solid system is entirely supported by thebeam of the electrobalance; the variations in Archimedean thrust thusrelate to the entire weight of the container and this is liable toaffect the sensitivity of the balance since this latter is subjected toa fairly substantial weight.

In another alternative embodiment which will now be described, thedisadvantages mentioned in the foregoing are overcome by dispensing withthe inert liquid and concurrently increasing the accuracy of themeasurement.

In the second alternative embodiment, control of the solidification of atwo-phase liquid-solid system essentially consists in determining thevariation in volume related to the solid-liquid transformation bypartially immersing in the liquid phase a plunger which is maintained ina substantially stationary position, in then measuring the variations inArchimedean thrust on said stationary plunger with respect to thecontainer which is also stationary; the variations in Archimedean thrustare due to the variations during solidification in the level of theliquid which is present above the crystal; these variations in level ofthe liquid result from the differences between the specific weights ofthe liquid and of the solid which are transformed one into the otherduring crystallization.

The plunger employed has a regular shape and especially a cylindricalshape with calibrated dimensions, a density which is higher than thedensity of the liquid undergoing crystallization and is supported by awire attached to one of the arms of the beam of an electrobalance. It isreadily apparent that the weight of the plunger is independent of thequantity of crystal to be formed, which was not the case in theembodiment described in the main patent. Thus only the resultant weightin relation to the depth of an immersion of the plunger and therefore tothe quantity of crystal formed is recorded by the electrobalance.

The method which relates to the device in accordance with this secondalternative embodiment applies to all methods of solidification of amixture (growth of homogeneous crystals) wherein the stationarycontainer in which the solid-liquid system is present duringcrystallizaton is placed within a furnace which is maintained at aconstant temperature gradient by regulating means or any other suitablemeans and which is programmed so as to permit of controlled cooling.

In FIG. 5, the container 102 is filled with a liquid 104 whichcrystallizes so as to form the crystal 106 under the influence of atemperature gradient (not shown) which is obtained in a conventionalmanner under the influence of heating means 108, said heating meansbeing programmed electrically so as to produce a variation in thefalling temperatures as a function of time. A heat-resistant casing 110surrounds the temperature-gradient furnace together with its electricalheating means 108 and isolates said furnace from the exterior. A plunger112 is partially immersed in the liquid bath 104 which is the bath ofliquid to be crystallized; the plunger is suspended by means of the wire114 on the beam 116 of an electrobalance 118.

The plunger 112 and the container 102 are maintained in a stationaryposition by means which are related to the principle of operation of theelectrobalance (zero instrument). After preliminary adjustment andbalancing of the current within the electrobalance in respect of apredetermined position of the plunger, a measurement is taken of thevariations in Archimedean thrust caused by the variations ΔL_(m) in thelevel of the surface of the liquid within the container duringcrystallization. This measurement of Archimedean thrust makes itpossible to follow the growth of the crystallization process. As in thefirst alternative embodiments, the parasitic forces (capillary tension,variation in thrust due to the variation in mean density of the liquid,variation in dimensions of the plunger and of the container and soforth) are eliminated by the use of the differential method.

The respective cross-sections of the crucible and of the plunger can bechosen in order to produce a predetermined amplitude of the measuredArchimedean thrust and therefore to achieve enhanced accuracy. Thisadvantage can be shown by the following simplified formula: ΔL_(m)=ΔV/S-s which indicates that, in the case of a variation in volume ofthe sample ΔV resulting from modification of part of the liquid, thevariation in thrust which is directly proportional to the variation inmeasured depth of immersion ΔL_(m) will be greater as the cross-sections of the plunger comes closer to that of the crucible S.

As mentioned in the foregoing, the load applied to the beam of theelectrobalance is essentially the weight of the plunger 112 reduced bythe Archimedean thrust over the immersed depth and not, as in the deviceshown in FIG. 1, the weight of the solid-liquid container assemblyreduced by the Archimedean thrust exerted by the inert liquid whichsurrounds said assembly.

What we claim is:
 1. Apparatus for controlling the directionalsolidification of a two-phase liquid-solid system wherein thesolidification is by cooling of and occurs in the liquid phase, saidapparatus comprising:a container for holding the liquid-solid system;heating means for producing a thermal gradient of regulated value withinsaid container; means for measuring variations in the volume of theliquid-solid system resulting from changes in molar volume due totransfer between liquid and solid phases in the system during thesolidification; and means for regulating said thermal gradientresponsive to said measured variations in the volume of the liquid-solidsystem.
 2. Apparatus for controlling the directional solidification of atwo-phase liquid-solid system wherein solidification is by cooling ofand occurs in the liquid phase, said apparatus comprising:a first opencontainer for holding an inert liquid; heating means for producing athermal gradient of regulated value within said first container; asecond open container containing the liquid to be solidified, saidsecond container being immersed in the inert liquid of said firstcontainer, the inert liquid and the upper surface of the liquid to besolidified being in contact; means for measuring variations in theapparent weight of said second container and its contents, saidvariations in apparent weight being due to changes in buoyancy of thesecond container and its contents resulting from changes in the volumeof its contents which occur during mass transfer from the liquid phaseto the solid phase during solidification; and means for regulating saidthermal gradient responsive to said measured variations in apparentweight.
 3. The apparatus of claim 2 wherein said means for measuringvariations in apparent weight is an electro-balance.
 4. The apparatus ofclaim 3 wherein said means for measuring variations in the apparentweight delivers a first electrical signal and wherein said means forregulating said thermal gradient comprises means for measuringtemperature and delivering a second electrical signal representative ofsaid temperature and means for comparing said first and secondelectrical signals.
 5. Apparatus for controlling the epitaxial growth ofa solid, from liquid phase, on a crystalline substrate, said apparatuscomprising:an elongated housing; a pair of elements slidably mountedwithin said housing and defining a space therebetween for containing theliquid; at least one recess in said housing for holding the crystallinesubstrate for contact with the liquid; a capillary tube mounted on saidhousing, the lower end of said capillary tube opening into the interiorof said housing for communication with said liquid containing space;means for measuring variations in the level of the liquid meniscus insaid capillary resulting from charges in volume of the contents of spacewhich occur during mass transfer from the liquid phase to the solidphase during solidification on the substrate; and heating means forcontrolling the temperature within said housing responsive to saidmeasured variations in meniscus level.
 6. The apparatus of claim 5wherein said means for measuring variations in the miniscus leveldelivers a first electrical signal and wherein said means forcontrolling temperature comprises means for measuring temperature anddelivering a second electrical signal representative of said temperatureand means for comparing said first and second electrical signals. 7.Apparatus for controlling the directional solidification of a two-phaseliquid-solid system wherein solidification is by cooling of and occursin the liquid phase, said apparatus comprising:an open container forholding the liquid undergoing solidification; a plunger having a densitygreater than that of the liquid and means for suspending the plunger ina stationary position partially immersed in the liquid: means formeasuring variations in the apparent weight of siad plunger due tochanges in the bouyant force of the liquid on the stationarilypositioned plunger produced by changes in liquid level, said changes inliquid level resulting from changes in the volume which occur duringmass transfer from the liquid phase to the solid phase duringsolidification; and heating means for controlling the temperature withinsaid container responsive to said measured variations in apparentweight.
 8. The apparatus of claim 7 wherein said plunger is cylindrical.9. The apparatus of claim 7 wherein said means for measuring changes inapparent weight is an electro-balance from one arm of which the plungeris suspended.
 10. The apparatus of claim 7 wherein said means formeasuring variations in the apparent weight delivers a first electricalsignal and wherein said heating means comprises means for measuringtemperature and delivering a second electrical signal representative ofsaid temperature and means for comparing said first and secondelectrical signals.